Enter the input variable value in the selected currency.
Enter the percentage change range.
Enter the target function result.
History:

Explanation

What is Sensitivity Analysis?

Sensitivity analysis is a technique used to determine how different values of an input variable can impact a particular output variable under a given set of assumptions. It helps in understanding the relationship between input and output variables, allowing users to identify which inputs have the most influence on the output.

How to Use the Sensitivity Analysis Calculator?

The Sensitivity Analysis Calculator requires three main inputs:

  1. Input Variable Value (a): This is the initial value of the variable you want to analyze.
  2. Change Range (%): This represents the percentage change you want to apply to the input variable. It can be both positive and negative.
  3. Target Function Result (b): This is the expected result of the function based on the input variable.

The calculator will then compute:

  • Lower Bound: The minimum expected value of the input variable after applying the change range.
  • Upper Bound: The maximum expected value of the input variable after applying the change range.
  • Sensitivity: The percentage change in the target function relative to the input variable.

Formulas Used:

  1. Lower Bound Calculation: §§ \text{Lower Bound} = a \times \left(1 - \frac{\text{Change Range}}{100}\right) §§

  2. Upper Bound Calculation: §§ \text{Upper Bound} = a \times \left(1 + \frac{\text{Change Range}}{100}\right) §§

  3. Sensitivity Calculation: §§ \text{Sensitivity} = \frac{b - a}{a} \times 100 §§

Where:

  • § a § — Input Variable Value
  • § b § — Target Function Result
  • § Change Range § — Percentage change applied to the input variable

Example:

Let’s say you have an input variable value of $100, a change range of 10%, and a target function result of $150.

  1. Input Variable (a): $100
  2. Change Range: 10%
  3. Target Function (b): $150

Calculations:

  • Lower Bound: §§ \text{Lower Bound} = 100 \times \left(1 - \frac{10}{100}\right) = 90 §§

  • Upper Bound: §§ \text{Upper Bound} = 100 \times \left(1 + \frac{10}{100}\right) = 110 §§

  • Sensitivity: §§ \text{Sensitivity} = \frac{150 - 100}{100} \times 100 = 50% §§

When to Use the Sensitivity Analysis Calculator?

  1. Financial Modeling: To assess how changes in assumptions affect financial projections.
  2. Project Management: To evaluate risks and uncertainties in project outcomes.
  3. Investment Decisions: To analyze how variations in market conditions impact investment returns.
  4. Scientific Research: To understand how changes in experimental conditions affect results.
  5. Business Strategy: To determine the impact of different strategies on business performance.

Practical Applications

  • Investment Analysis: Investors can use this calculator to understand how changes in market conditions might affect their portfolio returns.
  • Budgeting: Businesses can analyze how fluctuations in costs or revenues impact their overall financial health.
  • Product Development: Engineers can assess how variations in material properties affect product performance.

Definitions of Key Terms

  • Input Variable: The initial value that is subject to change in the analysis.
  • Change Range: The percentage by which the input variable is expected to change.
  • Target Function: The outcome or result that is being analyzed in relation to the input variable.

Use the calculator above to input different values and see how the sensitivity analysis changes dynamically. The results will help you make informed decisions based on the data you have.